
Problem 53
Calculate the
values and draw
the diagrams for shearing force and
bending moment for the following
overhanging beam shown in figure
53(a).
Figure 53(a)
Solution:
The freebodydiagram is shown in
figure 53(b). The
unknown reaction components of the beam are calculated
in
Prob
42
as A_{x}=0, A_{y} = 10 kN and B_{y}
= 55 kN; Shearing force calculations
In case of point load acting at a point, we
should calculate shear force on both sides (left and right) of the
point.
F_{A}left =
0;
F_{A}right
= 10 kN;
F_{C} = 10
kN;
F_{B}left =
10 – 5x4 =  30 kN;
F_{B} right
= 10 – 5x4 + 55 = +25 kN;
F_{D}left =
+25 kN;
F_{D}right
= +2525 = 0;
The values of shear
force are plotted in SFD in figure 53(b)
Bending moment
calculations
M_{A} = 0;
M_{C} = 10x2
= 20 kNm;
M_{B} = 10x6
– 5x4x2
= 60 40 = 100 kNm;
M_{D} = 0;
The values of bending moment are plotted in BMD.in
figure 53(b) 
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The bending moment
diagram shows that bending moment is hogging throughout the span of
the beam and maximum BM is at B (shear force changes sign at B). The
bending moment diagram is straight line from A to C (due to point
load), parabolic from C to B (due to udl) and straight line from B
to D (due to point load). It is important to note that the parabola
is a increasing parabola (means slope is increasing) because the
shear force is increasing from C to B. Rate of change of bending
moment is equal to shear force.
More examples on shear and moment diagrams
Example 51
Example 52
Example 54
You can also use our Free online calculators given below
(i)
bending moment & shear force calculator for
Cantilever
(ii)
Bending moment & shear force calculator
for Simple supported beam
(iii)
Bending moment & shear force calculator
for Overhanging beam
(iv)
Bending moment & shear force calculator for Fixed beam
(v)
Calculator for Continuous beam
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